Explanation:
To calculate the 99% one-day expected shortfall (ES), we first need to determine the Value at Risk (VaR).
The 99% VaR for a sample of 500 trading days corresponds to the tail of the worst 1% of the observations. 1% of 500 = 5 observations.
The VaR is the 5th worst loss, which is 6,712. The expected shortfall (ES) is the average of the losses in the 1% tail (i.e., the worst 5 losses).
Worst 5 losses: 9,111, 8,669, 8,127, 7,098, 6,712. Average = (9,111 + 8,669 + 8,127 + 7,098 + 6,712) / 5 = 39,717 / 5 = 7,943.4.
Rounding to the nearest whole number, we get 7,943.
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Q.10 Jimmy Ray, a risk analyst at Alcoa Bank, has just performed a historical simulation for estimating the VAR for the fixed-income portfolio of the bank based on the returns for the last 500 trading days. The 10 worst one-day returns generated in the simulation are:
-9,111, -8,669, -8,127, -7,098, -6,712, -6,698, -5,743, -5,189, -4,811, -4,775
Which of the following is the 99% one day expected shortfall for the portfolio?
A
8,145
B
6,712
C
9,111
D
7,943
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